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The C2 and C4 longitudinal form factors for the first excited (21+) and (41+) states in the even-even Palladium isotopes ( 104 Pd, 106 Pd, 108 Pd, 110 Pd) and 90 Zr are compared in this work. We use three different nuclear potentials (Skyrme Sk35, Woods-Saxon (WS), and Harmonic Oscillator (HO)) in our theoretical calculations and compare them with real electron scattering data. The strengths and limits of each potential in explaining the observed form factors for quadrupole and hexadecapole transitions over a variety of nuclei are clarified by this comparison. Our research shows that the Skyrme Sk35 interaction, which suggests a more accurate description of the underlying transition density, often gives the most consistent agreement with experimental data, especially at greater momentum transfers. The observed discrepancies, particularly for C4 transitions and higher momentum transfers, highlight the difficulties in accurately modelling higher multipolarity excitations and point to the need for more sophisticated theoretical treatments that include effects other than simple mean-field descriptions, such as core polarization and meson exchange currents.

The Lagrangian that defines quantum chromodynamics (QCD), the strong interaction piece of the Standard Model, appears very simple. Nevertheless, it is responsible for an astonishing array of high-level phenomena with enormous apparent complexity, e.g., the existence, number and structure of atomic nuclei. The source of all these things can be traced to emergent mass, which might itself be QCD’s self-stabilising mechanism. A background to this perspective is provided, presenting, inter alia, a discussion of the gluon mass and QCD’s process-independent effective charge and highlighting an array of observable expressions of emergent mass, ranging from its manifestations in pion parton distributions to those in nucleon electromagnetic form factors.

This study examines inelastic electron scattering form factors for the 17O and 26Mg nuclei within the sd model space, accounting for excitations outside the 16O core. Shell model computations were conducted utilising the NuShellX@MSU software, applying an effective interaction w to ascertain energy eigenvalues and eigenstates. The eigenstates were utilised to compute one-body transition densities (OBTD) for further computations of inelastic electron scattering form factors. Core polarisation (CP) effects were incorporated into the computations using the Michigan three-range Yukawa interaction as the residual interaction for core polarisation matrix elements. The computed form factors were juxtaposed with empirical data acquired from nuclear data archives. We plotted theoretical and experimental form factors as functions of momentum transfer (q) in our analysis. The incorporation of core polarisation effects markedly enhanced the concordance between theoretical predictions and experimental results.

The dissipative spectral form factor (DSFF), recently introduced in Li et al. (Phys Rev Lett 127(17):170602, 2021) for the Ginibre ensemble, is a key tool to study universal properties of dissipative quantum systems. In this work we compute the DSFF for a large class of random matrices with real or complex entries up to an intermediate time scale, confirming the predictions from Li et al. (Phys Rev Lett 127(17):170602, 2021). The analytic formula for the DSFF in the real case was previously unknown. Furthermore, we show that for short times the connected component of the DSFF exhibits a non-universal correction depending on the fourth cumulant of the entries. These results are based on the central limit theorem for linear eigenvalue statistics of non-Hermitian random matrices Cipolloni et al. (Electron J Prob 26:1–61, 2021) and Cipolloni et al. (Commun Pure Appl Math 76(5): 946–1034, 2023).

In this work, the Whittaker wave functions were used to study the nuclear density distributions and elastic electron scattering charge form factors for proton-rich nuclei and their corresponding stable nuclei ( 10,8 B, 13,9 C, 14,12 N and 19,17 F). The parameters of Whittaker’s basis were fixed to generate the experimental values of available size radii. The Whittaker basis was connected to harmonic-oscillator basis through boundary condition at match point. The nuclear shell model was opted with pure configuration for all studied nuclei to compute aforementioned studied quantities except 10 B. For 10 B, the total spin is 3 + , therefore, there is a C2 component in empirical Coulomb form factor in addition to C0 component. The theory of core-polarization was applied to account such C2 contribution using Tassie, Bohr-Mottelson and valence models. The contribution of model space to C2 component was computed using Cohen-Kurath interaction. For exotic 8 B, 9 C, 12 N and 17 F nuclei, the Whittaker’s basis was applied only to the last exotic valence proton, on contrary to stable 10 B, 13 C, 14 N and 19 F which the Whittaker’s basis was applied to both last stable valence proton and neutron . It was seen that such treatment highly improved the calculated quantities in comparison with empirical data.

We report a precise measurement of the parity-violating asymmetry \\(A_{\\rm PV}\\) in the elastic scattering of longitudinally polarized electrons from \\(^{48}{\\rm Ca}\\). We measure \\(A_{\\rm PV} =2668\\pm 106\\ {\\rm (stat)}\\pm 40\\ {\\rm (syst)}\\) parts per billion, leading to an extraction of the neutral weak form factor \\(F_{\\rm W} (q=0.8733\\) fm\\(^{-1}) = 0.1304 \\pm 0.0052 \\ {\\rm (stat)}\\pm 0.0020\\ {\\rm (syst)}\\) and the charge minus the weak form factor \\(F_{\\rm ch} - F_{\\rm W} = 0.0277\\pm 0.0055\\). The resulting neutron skin thickness \\(R_n-R_p=0.121 \\pm 0.026\\ {\\rm (exp)} \\pm 0.024\\ {\\rm (model)}\\)~fm is relatively thin yet consistent with many model calculations. The combined CREX and PREX results will have implications for future energy density functional calculations and on the density dependence of the symmetry energy of nuclear matter.

A bstract In this work, we compute one-loop planar five-point functions in N = 4 super-Yang-Mills using integrability. As in the previous work, we decompose the correlation functions into hexagon form factors and glue them using the weight factors which depend on the cross-ratios. The main new ingredient in the computation, as compared to the four-point functions studied in the previous paper, is the two-particle mirror contribution. We develop techniques to evaluate it and find agreement with the perturbative results in all the cases we analyzed. In addition, we consider next-to-extremal four-point functions, which are known to be protected, and show that the sum of one-particle and two-particle contributions at one loop adds up to zero as expected. The tools developed in this work would be useful for computing higher-particle contributions which would be relevant for more complicated quantities such as higher-loop corrections and non-planar correlators.

The concept of tree or stem form has been central to forest research for over a century, playing a vital role in accurately assessing tree growth, volume, and biomass. The form factor is an essential component for expressing the shape of a tree, enabling more accurate volume estimation, which is vital for sustainable forest management and planning. Despite its simplicity, flexibility, and advantages in volume estimation, the form factor has received less attention compared to other measures like taper equations and form quotient. This review summarizes the concept, theories, and measures of stem form, and describes the factors influencing its variation. It focuses on the form factor, exploring its types, parameterization, and models in the context of various tropical species and geographic conditions. The review also discusses the use of the form factor in volume estimation and the issues with using default or generic values. The reviewed studies show that tree stem form and form factor variations are influenced by multiple site, tree, and stand characteristics, including site quality, soil type, climate conditions, tree species, age, crown metrics, genetic factors, stand density, and silviculture. The breast height form factor is the most adopted among the three common types of form factors due to its comparative benefits. Of the five most tested form factor functions for predicting tree form factors, Pollanschütz’s function is generally considered the best. However, its performance is often not significantly different from other models. This review identifies the “Hohenadl” method and mixed-effects modelling as overlooked yet potentially valuable approaches for form factor modelling. Using the form factor, especially by diameter or age classes, can enhance tree volume estimation, surpassing volume equations. However, relying on default or generic form factors can lead to volume and biomass estimation errors of up to 17–35%, underscoring the need to limit variation sources in form factor modelling and application. Further recommendations are provided for improving the statistical techniques involved in developing form factor functions.

The standard model of particle physics is a well-tested theoretical framework, but there are still some issues that deserve experimental and theoretical investigation. The Ξ resonances with strangeness S=−2, the so-called doubly-strange hyperon, can provide important information to further test the standard model by studying their electromagnetic form factors, such as probing the limitation of the quark models and spotting unrevealed aspects of the QCD description of the structure of hadron resonances. In this work, we review some recent studies of the electromagnetic form factors on doubly-strange hyperons in pair production from positron–electron annihilation experiment.

Semicircles and circular sectors are both ubiquitous in the natural realm. However, mathematically speaking they have represented an enigma since antiquity. In recent years, the author has worked in integral equations with sections of spheres as related to radiative heat transfer and their associated form factors, to the point of defining new postulates. The main theorems thus far enunciated refer to the radiative exchange between circles and half disks, but recently the possibility to treat circular sectors has arrived, thanks to the research already conducted. As is known, to find the exact expression of the configuration factor by integration is complex. In the above mentioned problem of the circular sectors, the author reached the first two steps of the basic formulation for radiant exchange. Subsequently, the novelty of the procedure lies in introducing a finite differences approach for the third and fourth integrals which still remain unsolved, once we have been able to find the preliminary integrals. This possibility had not been identified by former research and the output provides us with an ample variety of unexpected scenarios. As a consequence, we are able to analyze with more precision the spatial transference of radiant heat for figures composed of circular sectors. We already know that spherical shapes cannot be discretized with any accuracy. Therefore, we would be able to reduce a considerable amount of hindrance in the progress of thermal radiation science. Important sequels will be derived for radiation in the entrance to tunnels, aircraft design and lighting as well.